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LIV. Contribution to the Osmotic Theory of Solutions. By 

 the Earl of Berkeley, F.E.S., and 0. V. Bltkton, D.Sc. 

 (London) *. 



IN the following communication our aim has been to 

 obtain exact relations between the various quantities 

 involved in osmetics, without making any assumption about 

 the properties of, or even the separate existence of the com- 

 ponents forming the solution f. In other words, we have 

 tried to express the osmotic phenomena in terms of the 

 physical properties of the solution itself. 



Although Kothmund J postulates two osmotic pressures 

 for liquid mixtures, yet it seems to have been overlooked 

 that any solution whatever (necessarily containing two com- 

 ponents) must have more than one osmotic pressure. As 

 pointed out by one of us §, besides the ordinary osmotic 

 pressure of an aqueous solution of sugar, realizable by 

 means of a copper ferrocyanide membrane, there is another 

 which would be realizable if we could place the solution in 

 communication with liquid sugar (say at its melting-point) 

 through a membrane permeable to the sugar only. It is 

 probable that this complementary osmotic pressure has been 

 ignored because it was assumed that the, properties of the 

 liquid solute were involved, and when the solute was un- 

 known in the liquid state it may have been argued that this 

 pressure was imaginary. 



In this paper, however, we shall establish a relation between 

 the two osmotic pressures which, as above stated, only 

 involves the physical properties of the solution, thus proving 

 that in so far as the ordinary osmotic pressure may be 

 regaided as a real physical quantity, the complementary 

 pressure can be similarly so regarded || . We shall also obtain 

 a relation applicable to the final stratification of any solution 

 when subjected to gravity or other steady bodily force. 



These relations will be established in two ways : first by 

 the consideration of a column of solution in static osmotic 

 equilibrium ; secondly, by a brief examination of the dynamic 

 processes involved in the progress towards that equilibrium. 



This latter method evidently touches on the theory of 



* Communicated by the Authors. 



t This is of some little importance, for, in many chemical reactions, 

 it has been proved that a solution may contain substances which cannot 

 he isolated. 



% Zeit. Phys. Ckem. vol. xxvi. p. 433 (1898). 



§ Proc. Boy. Soc, Series A, vol. lxxix. p. 129. 



|| One of us (C. V. B.) would limit this statement to its differential 

 aspect. 



